What exactly is the relationship between the magic classes?

[Design]

So,

Basically are they all trying to help each other? Hurt each other? Save each other? One trying to suppress the other's magic?

[Catapult]

So,

Basically are they all trying to help each other? Hurt each other? Save each other? One trying to suppress the other's magic?

It would be more accurate to say they compliment each other. I'll try and explain this from my own perspective, which is a very different angle.

Conjury is the magic of nature. It weaves the aether of nature to manipulate nature, thus making it dependant upon an understanding of nature and its elemental guardians. Earth is uplifted, air is moved and water is gathered. Curing magic re-forms the body to close wounds (enhanced in WHM). It is the magic of motion.

Thaumaturgy is the magic of raw energy. It draws forth the aether of one's own wellspring and by regulating their aether in the astral and umbral polarities, are able to channel the latent aether of the world (and void - BLM) through themselves and into an expression of energy. This takes the form of electrical currents, burning heat, or the icy absence there of.

Arcanima is the magic of matter-alteration. Through the use of symbols, they apply aether to transform the environment around them. This can inflict disease and slowly tear at a victim's biology. It can also cause the aether around them to transform into an entity that bear's the consciousness of aether (much like how a primal is summoned but on a smaller scale) and bind it to their will. This bears a greater similarity to ancient Allagan techniques, which may have persisted in Nym and the Southern Island areas in isolation from the Black/White advancements of mainland Eorzea.

Motion, Energy and Matter. Three ways of manipulating aether, all with very different results.

[RoboPadre]

Catapult, I believe that is the most succinct explanation of all three schools I have seen thus far.

And, Design, it would be more accurate to say that they don't really feel all too much toward the other. Perhaps a sort of arrogance of "My school is better than your school," but, from what I've read in-game, the other schools could cease to be and one wouldn't care or notice too much.

[Design]

So pretty much each thinks they are right and the others are wrong?

[Rannie]

Since we suck the aether out of the atmosphere(which is not environmentally friendly compared to the other spell schools) to cast spells and since aether flows in living things I bet casting our major spells causes some trees or flowers to die around us. XD

I know this is completely off topic but when you said that I pictured the Giant Mega Maid from Spaceballs and Skroob Dark Helmet and the other guy going, "Suck suck suck suck"

btw catapult great explaination

[Enkidoh]

So,

Basically are they all trying to help each other? Hurt each other? Save each other? One trying to suppress the other's magic?

As Catapult said, they're basically in a mutual balance - although there is a certain amount of apparent rivalry between the three mage guilds, because each actually has a different role in their respective countries, it's not really a case of 'we're better than you'.

[Design]

If you are wondering, this is all for RP. My main is ARC and my "brother" is THM. So we were trying to figure out exactly what types of behavior and status each one has (I may actually be changing to CNJ)

[Nialle]

ACN sees their magic as more 'math-y and scientific', THM is more 'raw destruction (and maniacal laughing)', and CONJ is more 'peacefully at one with nature and all life'.

At least that was my impression of the guilds.

[Catapult]

Indeed no conflict, but using the techniques of one school will have limited effect in another. For example, using Thaumaturgical techniques to move the earth would require a lot more energy and focus as it takes a great deal of power to move things, compared to making lightning dance across things. And trying too hard could kill you (ref: Sylphie).

PS: ARC = Archer. Arcanist = ACN.

[Enkidoh]

Also, as per my earlier post, each Guild actually serves a more social/mundane role in their respective nation, where their magical abilities are put to other uses other than warfare:

The CNJ's Guild is used to intercede between the Gridanians and the elementals on mundane matters, due to the treaty between the elementals and Gridania, the elementals insist that anything that would impact on the forest has to have the permission of the elementals first, and hence, the CNJ's fill this role, specifically CNJs especially sensitive to the elementals' whisperings who are known as 'hearers'. Accordingly, the CNJ's Guild also plays an important part in Gridania's government the Seedseer Council.
The THM's Guild are essentially funeral directors who developed their school of magic from their funerary rites (the guild receptionist clearly states this early on when you first join up), although a lot of Ul'dahns hold them in contempt as there have been rumours they demand elaborate funerals simply to graverob the deceased after the service.
The ACN's Guild are effectively the Customs house for Limsa Lominsa - although it's somewhat obscure exactly how they would use Arcanamia in this way, I presume it would be used to screen incoming goods for contraband without opening crates, or something. But I have no conclusive evidence in that regard so take that with a grain of salt.

As for Sylphie, as was stated she was using her own life force to power her healing spells, of which her spell potency seemed to be in equality with how much of her 'life' she used (hence why E-Sumi Yan expressly forbid her to use Raise - as Raise restores the (presumably recently) dead to life, if she used it it would have given life at the cost of her own.).